Super Safi’s Monday Morning Math Mayhem 12 – Fractions

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

 

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

While celebrating Pi day a couple weeks ago, we discussed how it is an irrational number that cannot be expressed as a fraction. This week we look at fractions.

 

Fractions

A fraction represents a part of a whole. It comes from the latin word fractus, meaning broken. Fractions are commonly expressed in the form a/b, where b is not equal to 0. In the form a/b, a is known as the numerator and b as the denominator.

As far back as 4,000 years ago, the Egyptians used what is now known as Egyptian fractions. Egyptian fractions are reciprocals of integers. Egyptian fractions were 1/2, 1/3, 1/4, 1/5, … However, they did not use the modern day a/b notation that is now used.

The a/b notation with a horizontal bar separating the numerator and denominator dates back to the 12th century when Muslim mathematician Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar (better known as just Al-Hassar) first used the notation in Moracco. His notation quickly became popular and was widely used in the following century, most notably thanks to Italian mathematician Leonardo Fibonacci (pictured below). Fibonacci popularized the Hindu–Arabic numeral system in the Western World primarily through his 1202 publication of Liber Abaci, meaning Book of Calculation.

 

In Postcards From the Wedge (Season 21, Episode 14), Bart tells us how much he detest fractions:

Bart:  “I would end all life on this planet just to get out of doing fractions.”
Lisa:  “Fractions aren’t that hard. You just have to have a common denominator. For example, one-half plus one-third equals three-…”
Bart:  “End. all. life. on. this. planet!” [makes explosion sound]
Lisa:  “You’ll need to know fractions to make that explosion!”

But only three seasons later, in Adventure’s in Baby-Getting (Season 24, Episode 03), after Homer fails to fix a leak in the hose faucet, the ground under Springfield collapses from the mass of the pooling water and causes a sinkhole in the middle of the city. Marge, Lisa, and Bart are driving to school when Marge’s car falls through the sinkhole as the ground collapses and ruins her car. But just before the car falls through, we get a glimpse at Bart’s math homework.

 

Like Lisa said, fractions aren’t hard, you just need to find a common denominator (for addition and subtraction). Fortunately for us, every question has a common denominator. Lets go ahead and work through Bart’s homework.

 

Adding Fractions

When adding fractions with common denominators, you simply have to add the numerators to obtain the new numerator, while the denominator remains the same. Questions 1 and 4 feature addition:

5/8  +  1/8  =  6/8   (6/8 can be reduced by dividing both numerator and denominator by 2 to get 3/4)

4/12  +  7/12  =  11/12

Subtracting Fractions

Subtracting fractions is essentially the same as adding. When subtracting fractions with common denominators, you simply have to subtract the numerators to obtain the new numerator. Question 2 features subtraction:

3/7  –  2-7  =  1/7

Multiplying Fractions

Multiplying fractions does not require common denominators. You simply multiply the numerators to obtain the new numerator and multiply the denominators to obtain the new denominator. Question 5 features multiplication:

3/6  x  7/6  =  21/36  (21/36 can be reduced by dividing both numerator and denominator by 3 to get 7/12)

Dividing Fractions

Dividing fractions, like multiplying fractions, does not require common denominators. You simply multiply the first fraction by the reciprocal of the second fraction. Question 3 features division:

5/4  ÷  3/4  =  5/4  x  4/3  =  20/12  (20/12 can be reduced by dividing both numerator and denominator by 4 to get 5/3)

 

Now that we’ve got a better understanding of fractions and looked at Bart’s homework, are you reminded of your days in math class? Did you remember this episode? Were you able to solve the problems on your own? Do you enjoy calculating with fractions? Sound off in the comments below. You know we love hearing from you.

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13 responses to “Super Safi’s Monday Morning Math Mayhem 12 – Fractions

  1. I’ve loved math for as long as I can remember. So much so that I became a HS math teacher. My personal favorite is imaginary numbers. I have used Simpsons and the lottery as a project on probability.

    Liked by 1 person

  2. it brings memories of when I was just a young lad.. not knowing math and with no hair in my chest… some things change, now I know some math.

    Liked by 1 person

  3. Brings back memories !!!

    Liked by 1 person

  4. I’m trying to figure out what Lisa’s answer would be, given that she was interrupted after saying “three-…” instead of “five-…”

    Liked by 1 person

  5. I’d completely forgotten how to devide fractions….got that one wrong.
    :o(
    You mentioned Fibonacci in this post. Is that foreshadowing? Fibonacci numbers and how they relate to music?
    ~MIB👤

    Liked by 2 people

  6. I always looked at math as a language, just like Spanish or French. If you get a good solid vocabulary (adding, subtracting, fractions etc), then making paragraphs (algebra) amd whole essays (physics) is not quite as daunting. I was lucky to have excellent math teachers when I was in elementary school, so I was able to keep building on that base. By the time I got to college, I ended up tutoring most of my friends in math and physics. I always tried to take them back to where they first started to stumble…whether it was Jr High, High School or even Elementary school… then work forward, just like a language teacher.
    I never found any person that was “too stupid” to do math, only people who got lost early on and never were able to catch up. Once they were comfortable with basic math vocabulary, everything else started to come easier. So…if you think you’re one of those people who “just can’t get” math (I’m talkin to you, Bart), maybe try going back to the basics and work forward. Yes, it takes a little time (and you do have to memorize the basics, just like you learned the alphabet), but it always takes a while to get comfortable with a new language. There’s no shame in trying again to master the basics…ask any Spanish teacher.😁

    Liked by 3 people

    • Wouldn’t Bart say desperately “Lisa HELP me”?

      Liked by 1 person

    • Tracy-1ltwoody920

      I too stumbled in math, until 5th or 6th grade.
      And in 6th I was among the elite that was pushed into the
      Some Math Some Garbage Yellow Book.
      SMSG

      Subtract 39 from 62
      How does one subtract 9 from 2?
      Mom tells me “borrow from the 6 to make the 2 a 12”
      I reply “the 6 can’t loan”

      SMSG teaches:
      You are subtracting 3 units of ten and 9 units of one, from
      6 units of ten and 2 units of one.
      And show your work!!!

      Poor teaching made it into a process – but once I understood the concepts.
      Math was a natural as breathing.

      Liked by 1 person

  7. It has been a long time ago, but I did get all of them right 😁

    Liked by 1 person

  8. Thanks a lot Safi! I’m glad we found this… common denominator.

    Liked by 2 people

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